The increasing complexity of interrelated systems has made the use of multiplex networks an important tool for explaining the nature of relations between elements in the system. In this paper, we aim at investigating various aspects of countries' behaviour during the coronavirus pandemic period. By means of a multiplex network we consider simultaneously stringency index values, COVID-19 infections and international trade data, in order to detect clusters of countries that showed a similar reaction to the pandemic. We propose a new methodological approach based on the Estrada communicability for identifying communities on a multiplex network, based on a two-step optimization. At first, we determine the optimal inter-layer intensity between levels by minimizing a distance function. Hence, the optimal inter-layer intensity is used to detect communities on each layer. Our findings show that the community detection on this multiplex network has greater information power than classical methods for single-layer networks. Our approach better reveals clusters on each layer with respect to the application of the same approach on each single-layer. Moreover, detected groups in the multiplex case benefit of a higher cohesion, leading to identifying on each layer a lower number of communities with respect to the ones obtained in the single-layer cases.
